Place the four steps of the elimination method in the proper order. if equal, subtract the equations. if opposite, add the equations. find the variable with equal or opposite coefficients. substitute the known value into the other equation and solve for the remaining variable. solve the resulting one-variable equation

The steps for solving a system of equations using elimination are:

1. Find the variable with equal or opposite coefficients.
2. If equal, subtract equations. If opposite, add the equations.
3. Solve the resulting one-variable equation.
4. Substitute the known value into the other equation and solve for the remaining variable.

Let's attempt solving a system using these steps.

     2x + 4y = 8
    -2x + 6y = 2

First step: Find the variable with equal or opposite coefficients.

The variable terms with equal or opposite coefficients are the x-terms - they are 2x and -2x  (opposite terms).

Second step: If equal, subtract equations. If opposite, add the equations.

The coefficients are opposite, thus we must add the equations.

     2x + 4y = 8
    -2x + 6y = 2
+
       0 + 10y = 10

Third step: Solve the resulting one-variable equation.

    0 + 10y = 10
          10y = 10
              y = 1

Fourth step: Substitute the known value into the other equation and solve for the remaining variable.

       -2x + 6y = 2
    -2x + 6(1) = 2
        -2x + 6 = 2
              -2x = -4
                 x = 2

The solution to this system is (2, 1).